To determine the median salary for a company with 100 employees, we need to arrange all salaries in ascending order and find the middle value. The median is a measure of central tendency that represents the middle point of a dataset.

Understanding the Median Concept

The median is the value separating the higher half from the lower half of a data sample. When dealing with a dataset, the first step is always to arrange the data in ascending (or descending) order. The method for finding the median depends on whether the total number of data points (N) is odd or even.

• If N is odd, the median is the value at the \( \left( \frac{N+1}{2} \right) \)-th position.
• If N is even, the median is the average of the values at the \( \frac{N}{2} \)-th and \( \left( \frac{N}{2} + 1 \right) \)-th positions.

In this company, we have a total of 100 employees, which means N = 100. Since N is an even number, the median salary will be the average of the 50th and 51st salaries when all salaries are listed in ascending order.

Analyzing Salary Distribution in the Company

Let's list the salary ranges and the number of employees earning within each range to understand the company's salary distribution. We will also track the cumulative number of employees to easily locate the 50th and 51st salaries.

Calculating the Median Salary

From the table above, we can identify the position of the 50th and 51st employees in the salary distribution:

• The first 45 employees earn Rs. 20,000.
• Employees from the 46th position up to the 70th position earn Rs. 30,000.

This means:

• The 50th employee's salary is Rs. 30,000.
• The 51st employee's salary is also Rs. 30,000.

Now, we calculate the median by taking the average of these two salaries:

$$ \text{Median Salary} = \frac{\text{Salary of 50th Employee} + \text{Salary of 51st Employee}}{2} $$

$$ \text{Median Salary} = \frac{20,000 + 20,000}{2} $$

Wait, let's recheck the values. The 50th and 51st employees fall into the group earning Rs. 30,000. The calculation should be:

$$ \text{Median Salary} = \frac{30,000 + 30,000}{2} $$

$$ \text{Median Salary} = \frac{60,000}{2} $$

$$ \text{Median Salary} = 30,000 $$

Therefore, the median salary in the company is Rs. 30,000.